Question

Find the 20th term of the series $2\times 4+4\times 6+6\times 8+\dots \dots +n$ terms.

Answer 1

The given series is

$2\times 4+4\times 6+6\times 8+\dots \dots +\text{n terms}$

Let $a_n$ be the nth term of given series.

$\therefore a_n=\text{(nth term of 2,4,6....)}\text{(nth term of 4,6,8 ....)}$

$=[2+(n-1)\times 2][4+(n-1)\times 2]$

$=2n(2n+2)$

$\therefore a_{20}=2\times 20(2\times 20+2)$

$=40\left(42\right)=1680$